Lambda calculus provides a theoretical framework for describing functions and their evaluation. Although it is a mathematical abstraction rather than a programming language, it forms the basis of almost all functional programming languages today. An equivalent theoretical formulation, combinatory logic, is commonly perceived as more abstract than lambda calculus and preceded it in invention. It is used in some esoteric languages including Unlambda. Combinatory logic and lambda calculus were both originally developed to achieve a clearer approach to the foundations of mathematics.
An early functional flavored language was Lisp, developed by John McCarthy while at MIT for the IBM 700/7000 series scientific computers in the late 1950s. Lisp introduced many features now found in functional languages, though Lisp is technically a multi-paradigm language. Scheme and Dylan were later attempts to simplify and improve Lisp.
Information Processing Language (IPL) is sometimes cited as the first computer-based functional programming language. It is an assembly-style language for manipulating lists of symbols. It does have a notion of "generator", which amounts to a function accepting a function as an argument, and, since it is an assembly-level language, code can be used as data, so IPL can be regarded as having higher-order functions. However, it relies heavily on mutating list structure and similar imperative features.
Kenneth E. Iverson developed APL in the early 1960s, described in his 1962 book A Programming Language (ISBN 9780471430148). APL was the primary influence on John Backus's FP. In the early 1990s, Iverson and Roger Hui created J. In the mid 1990s, Arthur Whitney, who had previously worked with Iverson, created K, which is used commercially in financial industries.
John Backus presented FP in his 1977 Turing Award lecture "Can Programming Be Liberated From the von Neumann Style? A Functional Style and its Algebra of Programs". He defines functional programs as being built up in a hierarchical way by means of "combining forms" that allow an "algebra of programs"; in modern language, this means that functional programs follow the principle of compositionality. Backus's paper popularized research into functional programming, though it emphasized function-level programming rather than the lambda-calculus style which has come to be associated with functional programming.
In the 1970s ML was created by Robin Milner at the University of Edinburgh, and David Turner developed initially the language SASL at the University of St. Andrews and later the language Miranda at the University of Kent. ML eventually developed into several dialects, the most common of which are now Objective Caml and Standard ML. Also in the 1970s, the development of Scheme (a partly functional dialect of Lisp), as described in the influential Lambda Papers and the 1985 textbook Structure and Interpretation of Computer Programs, brought awareness of the power of functional programming to the wider programming-languages community.
In the 1980s, Per Martin-Löf dveloped intuitionistic type theory (also called Constructive type theory), which associated functional programs with constructive proofs of arbitrarily complex mathematical propositions expressed as dependent types. This led to powerful new approaches to interactive theorem proving and has influenced the development of many subsequent functional programming languages.
The Haskell language began with a consensus in 1987 to form an open standard for functional programming research; implementation releases have been ongoing since 1990.